The regulations of the International Federation of Lawn Tennis specify that tennis balls can only be endorsed and utilized for championships if they present:
a weight comprised between 57.71 and 58.47 g.
a diameter comprised between 6.35 and 6.67 cm.,
the ball not being able to drop by its own weight through a hole having a diameter of 6.54 cm., and being able to drop by its own weight through a hole having a diameter of 6.86 cm.
a rebound comprised between 134.6 and 147.3 cm., when the ball drops from a height of 254 cm. on a concrete slab.
Furthermore, the tennis balls must comply with deformation tests adapted to define the manner in which they behave in play, particularly when they are hit by the racket.
Up to 1968 a single deformation test was provided. With the aid of a so-called Stevens machine, it was to be determined whether, when a ball is subjected to a compression force of 8.165 kg., its crushing--its deformation--is comprised between 0.673 and 0.737 cm (0.265 and 0.290 inch).
At that time, the Federation of Lawn Tennis modified the conditions of this deformation test, the so-called "forward" test, by bringing to 0.56 cm. (0.220 inch) the minimum of "forward" deformation, and requiring that the measurements be made less than 2 hours after "precompression" tests, reducing the resistance to deformation.
At the same time, there was provided a second deformation test, the so-called "return" test, in which, immediately after a crushing of 2.54 cm., the ball while being subjected during its decompression to the same compression force of 8.165 kg., should have a deformation comprised between 0.89 and 1.08 cm (0.350 and 0.425 inches).
The Stevens machine comprises dials on which the numerals of deformation may be read in thousandths of an inch, and, in order to determine whether a ball complies with the regulations, it is necessary to check that the numerals indicated by the machine are comprised between 220 and 290 for the "forward" test and between 350 and 425 for the "return" test.
In order to be endorsed, all the balls, whether inflated or non-inflated, must satisfy these tests, comprising the modifications decided in 1968.
In 1968, the International Federation of Lawn Tennis was fully aware of the problems which the manufacturers were encountering in order to make non-inflated balls, preserving well enough their hardness or toughness, that is to say their resistance to deformation in the course of play. It is for this reason that the Federation of Lawn Tennis introduced the "return" test intended to show how the ball behaves after repeated deformations. On the other hand, by lowering to 0.56 cm. the minimal "forward" deformation, the Federation permitted, however with a certain reluctance, the use of non-inflated balls offering the characteristic of being "very hard" when new so as to remain sufficiently hard in the course of play.
Despite the work of the Federation of Lawn Tennis to define the behavior of tennis balls and in spite of the endeavours of various manufacturers, the tennis balls actually manufactured are not completely satisfactory.
Inflated balls, i.e., those whose cores are inflated to a pressure greater than atmospheric pressure, rapidly lose their excess pressure. Within some months or even some weeks, their rebound capacity is reduced and they become too "soft", their deformation figures exceeding the maximum permitted. The play with such balls becomes too slow.
Non-inflated balls may be stored for a several months. However, after some games they lose a part of their "hardness", or resistance to deformation, and they cease to "respond" suitably when they are hit energetically. For example, it was determined that balls utilized in an important tennis tournament displayed deformation numerals (measured with the Stevens machine) as high as 280 and 460 after only nine games. Although these balls appear "hard" upon impact when they are new, they become much too "soft" after only nine games.
On the other hand, the behavior during play of all the types of balls is strongly affected by changes in the outer surface of their textile covering.
The analysis of the fibers constituting the outer surface of the textile coverings of the tennis balls most generally utilized has given the following results:
for inflated balls:
55% by weight of wool fibers, PA1 45% of 6 to 20 denier nylon fibers: PA1 58% of wool fibers, PA1 32% of 15 denier nylon fibers, PA1 10% of 25 denier viscose fibers.
for non-inflated balls:
Concerning these data, by definition, the weight in grams of 9000 meters of a fiber is its denier size.
Formerly, wool fibers agglomerated in such manner as to form a felted, very compact covering having a very smooth outer surface were utilized exclusively.
At the present time, textile coverings for tennis balls still comprise quite a great proportion of wool fibers, agglomerated in such manner as to impart a relatively smooth appearance to the outer surface of the new tennis balls which, as it is well known, are rather difficult to control.
However, their outer surface does not long remain smooth in the course of the game. With textile coverings such as those presently made, the ends of numerous fibers become disengaged from other fibers and stand up more or less perpendicularly to the outer surface of the ball, which gives it a more or less hairy or dishevelled appearance.
After extended play with such balls, particularly on hard or gravelly surfaces, the disengaged fibers wear or break off and, after several sets, the outer surface of these balls becomes smooth again while the weight and diameter of each ball are substantially reduced.
Aerodynamic tests carried out in a wind-tunnel have shown that while the new balls have a drag of 90 to 95 g., at a speed of 100 km. per hour, their drag could increase up to 105 or 110 g. after several games, then decrease again down to a value of the order of 85 g., or even less, when fibers were detached or worn.
It is known that the drag of a spherical body is given by the formula: EQU T=1/2p.multidot.V.sup.2 .multidot.S.multidot.Cx,
in which
p is the density of the air,
V the relative speed of the air and of the spherical body,
S the section of the spherical body, S=(.pi.d.sup.2 /4), d being the diameter, and
Cx a coefficient determined by the surface of the spherical body.
Considering a new ball having a diameter of 6.6 cm. and a smooth surface, with corresponding drag of 95 g. at 100 km. per hour, it would be necessary, if the condition of the surface of this ball remained unchanged, to increase its diameter to 7.10 cm. in order to obtain a drag of 110 g. and to reduce it to 6.24 cm. in order to obtain a drag of 85 g.
This means that if a player starts to play with a ball having a diameter of 6.6 cm., after several games, he has the impression that the diameter of the ball has increased to 7.10 cm. while, after several sets, he has, on the contrary, the impression that the diameter of the ball has decreased to 6.24 cm. and that its weight is also reduced.
Considering that the speed of 100 km. per hour is easily exceeded, for example in the case of serves, and that any modification of the drag is much more perceptible at higher speeds, it is not surprising that the players complain of meeting with difficulties in adjusting their strokes sufficiently, in order to preserve a correct length of said strokes in spite of the great differences in trajectory resulting from modifications in the behavior of the balls.
Of course, after several games, the softening of the core of a non-inflated ball combines with the increase in the drag of the ball to make the game very slow, while, when the fibers of the textile covering of a tennis ball are torn or worn, the loss in weight of the ball combines with the reduction of drag to make the play of this ball very rapid.